Question: Simplify the following expression and state the condition under which the simplification is valid. $k = \dfrac{-9x^3 + 900x}{2x^2 + 26x + 60}$
First factor out the greatest common factors in the numerator and in the denominator. $ k = \dfrac {-9x(x^2 - 100)} {2(x^2 + 13x + 30)} $ $ k = -\dfrac{9x}{2} \cdot \dfrac{x^2 - 100}{x^2 + 13x + 30} $ Next factor the numerator and denominator. $ k = - \dfrac{9x}{2} \cdot \dfrac{(x + 10)(x - 10)}{(x + 10)(x + 3)}$ Assuming $x \neq -10$ , we can cancel the $x + 10$ $ k = - \dfrac{9x}{2} \cdot \dfrac{x - 10}{x + 3}$ Therefore: $ k = \dfrac{ -9x(x - 10)}{ 2(x + 3)}$, $x \neq -10$